Polynomial evaluation over finite fields: new algorithms and complexity bounds

TL;DR

This paper introduces new algorithms for polynomial evaluation over finite fields that outperform traditional methods for high-degree polynomials, with applications in Reed-Solomon code decoding.

Contribution

It presents novel evaluation algorithms with improved complexity bounds for large-degree polynomials over finite fields.

Findings

Evaluation complexity is lower than standard techniques for high-degree polynomials.

Applications to syndrome computation in Reed-Solomon decoding are demonstrated.

New bounds on algorithm efficiency are established.

Abstract

An efficient evaluation method is described for polynomials in finite fields. Its complexity is shown to be lower than that of standard techniques when the degree of the polynomial is large enough. Applications to the syndrome computation in the decoding of Reed-Solomon codes are highlighted.